Regularization of Ill-Posed Problems by Iteration Methods: 499 (Mathematics and Its Applications) - Softcover

Gilyazov, S.F. F.; Gol'dman, N.L.

 
9789048153824: Regularization of Ill-Posed Problems by Iteration Methods: 499 (Mathematics and Its Applications)
Softcover
ISBN 10: 9048153824 ISBN 13: 9789048153824
Verlag: Springer, 2010

Inhaltsangabe

Iteration regularization, i.e., utilization of iteration methods of any form for the stable approximate solution of ill-posed problems, is one of the most important but still insufficiently developed topics of the new theory of ill-posed problems. In this monograph, a general approach to the justification of iteration regulari­ zation algorithms is developed, which allows us to consider linear and nonlinear methods from unified positions. Regularization algorithms are the ’classical’ iterative methods (steepest descent methods, conjugate direction methods, gradient projection methods, etc.) complemented by the stopping rule depending on level of errors in input data. They are investigated for solving linear and nonlinear operator equations in Hilbert spaces. Great attention is given to the choice of iteration index as the regularization parameter and to estimates of errors of approximate solutions. Stabilizing properties such as smoothness and shape constraints imposed on the solution are used. On the basis of these investigations, we propose and establish efficient regularization algorithms for stable numerical solution of a wide class of ill-posed problems. In particular, descriptive regularization algorithms, utilizing a priori information about the qualitative behavior of the sought solution and ensuring a substantial saving in computational costs, are considered for model and applied problems in nonlinear thermophysics. The results of calculations for important applications in various technical fields (a continuous casting, the treatment of materials and perfection of heat-protective systems using laser and composite technologies) are given.

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Críticas

`The book will be useful for specialists who in their theoretical and applied investigations deal with ill-posed and inverse problems.'
Mathematical Reviews Clippings (2001)

Reseña del editor

Iteration regularization, i.e., utilization of iteration methods of any form for the stable approximate solution of ill-posed problems, is one of the most important but still insufficiently developed topics of the new theory of ill-posed problems. In this monograph, a general approach to the justification of iteration regulari­ zation algorithms is developed, which allows us to consider linear and nonlinear methods from unified positions. Regularization algorithms are the 'classical' iterative methods (steepest descent methods, conjugate direction methods, gradient projection methods, etc.) complemented by the stopping rule depending on level of errors in input data. They are investigated for solving linear and nonlinear operator equations in Hilbert spaces. Great attention is given to the choice of iteration index as the regularization parameter and to estimates of errors of approximate solutions. Stabilizing properties such as smoothness and shape constraints imposed on the solution are used. On the basis of these investigations, we propose and establish efficient regularization algorithms for stable numerical solution of a wide class of ill-posed problems. In particular, descriptive regularization algorithms, utilizing a priori information about the qualitative behavior of the sought solution and ensuring a substantial saving in computational costs, are considered for model and applied problems in nonlinear thermophysics. The results of calculations for important applications in various technical fields (a continuous casting, the treatment of materials and perfection of heat-protective systems using laser and composite technologies) are given.

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Verlag
Springer
Erscheinungsdatum
2010
Sprache
Englisch
ISBN 10 
9048153824
ISBN 13 
9789048153824
Einband
Tapa blanda
Anzahl der Seiten
356
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
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Hamburg
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9780792361312: Regularization of Ill-Posed Problems by Iteration Methods (Mathematics and Its Applications, 499, Band 499)

Vorgestellte Ausgabe

ISBN 10:  0792361318 ISBN 13:  9780792361312
Verlag: Springer, 1999
Hardcover